# Hypothesis Testing - What to use to compare the product quality of two suppliers

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#### carvind

What will be the nature of the hypothesis (one-sided ot two-sided) if I need to compare the product quality of two suppliers?

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#### Stan Hilliard

I am assuming that you are testing the mean. If you only want to detect whether there is a difference it is a two-sided test. The test statistic is the difference in means.

If you plan to take action only if a specific supplier is higher/lower, then you can use a one-sided test - putting all of the alpha risk in one direction. Set it up such that rejection leads to the action.
Then the burden of proof will be attained before action is taken.

Stan

M

#### Marc Richardson

Perhaps a few words of preparation are in order. First of all, the populations from which the samples are drawn should be normaly distributed. It is also helpful to know whether the variances are equal prior to performing a T test on the sample means.
Marc Richardson

S

#### Stan Hilliard

When testing for the mean, the degree of normality of the population(s) is usually not of concern.

That is because the distribution of sample averages becomes normal as the sample size increases. Fortunately, even for populations with distributions that are quite non-normal, this effect is sufficient at a relatively small sample size -- like n=4 or n=5.

If it is suspected that the two suppliers produce different standard deviations, the variances can be compared with an F test. If significantly different, (or if the SDs are of practical difference size-wise) a modified t-test can be used -- like the Fisher-Behrens test.

However, depending on the situation, if one supplier exceeds the other in variability, that can be as important as a difference in means.

Stan

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